...There is no particular advantage to holding to a low ISO. ISO has nothing to do with exposure, only with the image that the camera will produce. I would set the ISO to "auto" or set a maximum setting, based on the camera's ability to deal with a lower signal-to-noise ratio (S/N). Do some testing with your camera to find out how much noise you get with each ISO setting. I seriously doubt if your shot will be spoiled by noise alone.
Ummmm... I would respectfully disagree. Given that this is a graduation photo, it's entirely likely that some will want to print it, and potentially at larger sizes. As well, given how small each face is going to be, even a bit of excess noise is going to have an effect as people zoom in to see themselves. You also need to consider exposure. It's a virtual certainty that some people will require local exposure adjustment due to shadowing, and increasing exposure on an already high ISO is a great way to turn an image to junk. Rather than allowing the camera to use auto, do some experimenting with your gear so that you know exactly what results you can expect at a given ISO, and keep it as low as practical.